Data mining for AI is presumably fair use, whereas when you sign up for a Claude account, you enter into a legally binding contract that says you will not distill a model based on its outputs.
"One color a day, told as it ought to be told: with its provenance, its chemistry, and the people who paid for it in poison." is so Claude it hurts. :'D
The point is also that you don't have to sign up for AWS, and GCP, and Azure, and Alibaba, and Nebius…
And, more importantly, that you can use the existing OpenAI SDK for your language but swap models (even across providers) by changing one line of code.
You're paying for convenience, yes, but model routers solve a real problem.
Using its own TERM is a deliberate design decision. I don't remember how to fix the terminal database, but it's pretty easy (your favorite search engine or LLM should be able to help you there).